Engineering applications of 2D and 3D finite element mesh generation in hydrogeology and water resources

Abstract

This paper develops an automatic density-controlled 2-D and 3-D finite element mesh generation system to solve practical engineering applications in geology, hydraulics, hydrology, water resources, etc. The Delaunay triangulation method is adopted to create triangular meshes based on the required density specified by users. A triangle-to-quadrilateral conversion method is used to generate quadrilateral meshes adaptively. Density control algorithms of adaptive 2-D mesh generation are presented to satisfy the various requirements of the overland and subsurface hydrogeology and water resources in the actual target area. According to the alignment of boundary edges and distribution of surface nodes, this paper proposes the main algorithm and basic criteria to generate supplementary triangle and quadrilateral meshes for filling the water regions of river reaches and junctions with storage. A stretch mode is proposed to generate triangular prism and hexahedral meshes by stretching the 2-D mesh into 3-D space based on the materials of geometric regions. The 1-D/2-D/3-D correspondence between the finite element mesh and the river reaches, junctions with and without storage, ponds, lakes, control structures and fractures is established. Finally, practical 2-D and 3-D meshing applications are provided to demonstrate the accuracy and effectiveness of the finite element mesh generator developed in this paper.